We investigate the mean curvature of semi-Riemannian graphs in the semi-Riemannian warped product $M\times f\mathbb{R}_\varepsilon$, where 𝑀 is a semi-Riemannian manifold, $\mathbb{R}_\varepsilon$ is the real line $\mathbb{R}$ with metric $\varepsilon dt^2(\varepsilon =\pm 1)$, and $f:M\to \mathbb{R}^+$ is the warping function. We obtain an integral formula for mean curvature and some results dealing with estimates of mean curvature, among these results is a Heinz–Chern type inequality.